Concept explainers
To find:
a. To build a model that expresses distance between two cars as a function of time .
Answer to Problem 19AYU
Solution:
a.
Explanation of Solution
Given:
Two cars are travelling perpendicular to each other with velocities 30 miles/hr and 40 miles/hr. One is 2 miles south of intersection and other is 3 miles east of intersection.
Calculation:
a. The motion of the cars can be represented as the figure below:
Let, be the velocity of the car travelling south = 30mph.
Let, be the velocity of the car travelling west = 40 mph.
Let, be the distance from the intersection at time of the car travelling south.
Let, be the distance from the intersection at time of the car travelling east.
The distance between the two cars at any time ‘’ can be written as
Substituting .
Therefore the distance between the cars at any time is .
To find:
b. Graph the function and find the value of at which is smallest.
Answer to Problem 19AYU
Solution:
b.
Explanation of Solution
Given:
Two cars are travelling perpendicular to each other with velocities 30 miles/hr and 40 miles/hr. One is 2 miles south of intersection and other is 3 miles east of intersection.
Calculation:
b. Graph the function and find the value of at which is smallest.
From the graph it can be seen that when , the distance between the cars ‘’ attains its minimum value . Therefore, is smallest when .
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